The animal bioassay today is a major source of data for studying the toxicity, carcinogenicity, and teratogenicity of chemical and environmental pollutants. Such data are usually analyzed by using some sort of dose response modeling. Furthermore the use of such data for risk assessment has become very important in recent year. The research planned in this proposal will attack statistical inference and analysis problems in for different areas relating to bioassay toxicity data. Specifically these are: 1.) developing dose response models for quantal response toxicity data and their use for low-dose extrapolation including a comprehensive computer program for risk assessment; 2.) studying estimation and testing problems in dose response models which incorporate time to response as well as dose from both a parametric and nonparametric approache; 3.) examining modeling and inference problems for dose response data from teratological or multigeneration studies; and 4.) developing C (Alpha) tests, their theory, and related procedures for bioassay toxicity data. The objective of this proposal is to develop new methods for analyzing toxicity data from chronic animal bioassays which meet more realistically some of the data problems arising in such studies. In particular, concern for the use of such data in risk assessment will be addressed.